{
  "id": "math/0110003",
  "version": "v2",
  "published": "2001-09-30T23:59:27.000Z",
  "updated": "2003-06-05T18:02:54.000Z",
  "title": "Regularity on abelian varieties I",
  "authors": [
    "Giuseppe Pareschi",
    "Mihnea Popa"
  ],
  "comment": "18 pages; final version, with substantial changes in the order of presentation in Section 2, and other minor expository changes, as suggested by the referee",
  "journal": "J. Amer. Math. Soc. 16 (2003), no.2, 285-302",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce the notion of Mukai regularity (M-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and strenghtens the usual Castelnuovo-Mumford regularity. Mukai regularity has a large number of applications, ranging from basic properties of linear series on abelian varieties and defining equations for their subvarieties, to higher dimensional type statements and to a study of special classes of vector bundles. Some of these applications are explained here, while others make the subject of upcoming papers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-06-05T18:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K05",
      "14K12"
    ],
    "keywords": [
      "abelian varieties",
      "mukai regularity",
      "higher dimensional type statements",
      "usual castelnuovo-mumford regularity",
      "vector bundles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10003P"
    }
  }
}